Study of dependency between the input noise and the parameter in fuzzy linear regression model

When noise exists in data, it is a very meaningful topic to reveal the dependency between the parameter h (i.e. the threshold value used to measure degree of fit) in Fuzzy linear regression (FLR) model and the input noise. In this paper, the FLR model is first extended to its regularized version, i.e. regularized fuzzy linear regression (RFLR) model, so as to enhance its generalization capability; then RFLR model is explained as the corresponding equivalent maximum a posteriori MAP problem; finally, the approximately inverse proportional dependency relationships that the parameter h with Laplacian noisy input and Uniform noisy input should follow are derived, respectively. Our experimental results also confirm this theoretical claim. We believe that this conclusion provides an important reference for us to determine h in FLR model with noisy input.